Apparatus for slurry and operation design in cuttings re-injection

Abstract

A system for simulating a wellbore used for cuttings re-injection, that includes functionality to obtain as input to the system at least one wellbore design parameter for the wellbore, at least one operating parameter for the cuttings re-injection, and a slurry design for a slurry to be injected into the wellbore, functionality to segment the wellbore into a plurality of elements, wherein each element includes a plurality of nodes, and functionality to perform a simulation at a current time interval. The functionality to perform the simulation includes functionality to update a solid accumulation at a bottom of the wellbore at the current time interval and functionality to perform for each of the plurality of nodes, until the wellbore reaches a steady-state condition for the current time interval, at least one calculation using the at least one wellbore design parameter, the at least one operating parameter, and/or the slurry design.

1. A computer system for simulating a wellbore used for cuttings re-injection, comprising:
 a processor; 
 a memory; 
 a storage device; and 
 software instructions to obtain as input to the system at least one wellbore design parameter for the wellbore, at least one operating parameter for the cuttings re-injection, and a slurry design for a slurry to be injected into the wellbore; 
 software instructions to segment the wellbore into a plurality of elements, wherein each element comprises a plurality of nodes; 
 software instructions to perform a simulation at a current time interval, wherein functionality to perform the simulation comprises:
 software instructions to update a solid accumulation at a bottom of the wellbore at the current time interval; 
 software instructions to perform for each of the plurality of nodes, until the wellbore reaches a steady-state condition for the current time interval, the following using the at least one wellbore design parameter, the at least one operating parameter, and the slurry design: 
 calculating a sliding bed velocity; 
 calculating a suspension cross-section area using the sliding bed velocity; 
 calculating an average suspension velocity using the suspension cross-section area; 
 calculating a solid particle velocity using the average suspension velocity; and 
 calculating a solid volume concentration in suspension using the solid particle velocity, and 
 
 software instructions for outputting simulation results. 
 
   
   
     2. The computer system of  claim 1 , further comprising:
 software instructions to obtain a simulation result after the steady-state condition is reached; 
 software instructions to determine whether the simulation result satisfies a criterion; 
 software instructions to modify at least one parameter selected from a group consisting of the at Least one wellbore design parameter for the wellbore, the at least one operating parameter for the cuttings re-injection, and the slurry design for a slurry to be injected into the wellbore to obtain a modified parameter; and 
 software instructions to repeat the simulation at the current time interval using the modified parameter. 
 
   
   
     3. The computer system of  claim 2 , wherein the criterion is the rate of solid accumulation in the wellbore. 
   
   
     4. The computer system of  claim 1 , wherein the steady-state condition is determined using a nodal solids mass for each of the plurality of nodes. 
   
   
     5. The computer system of  claim 4 , wherein the wellbore reaches the steady-state condition when the nodal solids mass for each of the plurality of elements converges. 
   
   
     6. The computer system of  claim 1 , wherein the slurry design comprises at least one selected from the group consisting of slurry rheology and size of particles in the slurry. 
   
   
     7. The computer system of  claim 1 , wherein the at least one operating parameter for the cuttings re-injection operating parameter comprises at least one selected from the group consisting of a cuttings re-injection pump rate and a shut-in time. 
   
   
     8. The computer system of  claim 1 , wherein the at least one wellbore design parameter for the wellbore comprises at least one selected from the group consisting of a wellbore depth, a wellbore diameter, a tubing property, a casing property, a depth of a top of a perforated interval in the wellbore, a depth of a bottom of a perforated interval in the wellbore, and a deviation angle of the wellbore. 
   
   
     9. The computer system of  claim 1 , wherein the plurality of elements are of equal size. 
   
   
     10. A computer system for simulating cuttings re-injection in a wellbore, comprising:
 a processor; 
 a memory; 
 a storage device; and 
 software instructions stored in the memory for enabling the computer system under control of the processor, to: 
 define a mass balance equation for a solids bed; 
 define a mass balance equation for a suspension solids; 
 segment the wellbore into a plurality of elements, wherein each element comprises a plurality of nodes; 
 segment a simulation into a plurality of time intervals; 
 for each of the plurality of time intervals:
 simulate cuttings re-injection to solve the mass balance equation for the solids bed and the mass balance equation for the suspension solids for each of the plurality of nodes, and 
 
 output the simulation results. 
 
   
   
     11. The computer system of  claim 10 , further comprising software instructions to:
 input at least one wellbore design parameter for the wellbore; 
 input at least one operating parameter for the cuttings re-injection; and 
 input a slurry design for a slurry to be injected into the wellbore, 
 wherein simulating the cuttings re-injection uses the at least one wellbore design parameter, the at least one operating parameter, and the slurry design. 
 
   
   
     12. The computer system of  claim 11 , wherein the slurry design comprises at least one selected from the group consisting of slurry rheology and size of particles in the slurry. 
   
   
     13. The computer system of  claim 11 , wherein the at least one operating parameter comprises at least one selected from the group consisting of a cuttings re-injection pump rate and a shut-in time. 
   
   
     14. The computer system of  claim 11 , wherein the at least one wellbore design parameter comprises at least one selected from the group consisting of a wellbore depth, a wellbore diameter, a tubing property, a casing property, a depth of a top of a perforated interval in the wellbore, a depth of a bottom of a perforated interval in the wellbore, and a deviation angle of the wellbore. 
   
   
     15. The computer system of  claim 10 , wherein solving comprises applying a finite difference method to iteratively solve the mass balance equation for the solids bed and the mass balance equation for the suspension solids for each of the plurality of nodes. 
   
   
     16. The computer system of  claim 10 , wherein the plurality of elements are of equal size. 
   
   
     17. The computer system of  claim 10 , wherein simulating the cuttings re-injection comprises determining whether each of the plurality of nodes is at a steady-state for one of the plurality of time steps. 
   
   
     18. The computer system of  claim 17 , wherein each of the plurality of nodes is at steady-state if a nodal solids mass for each of the plurality of nodes has converged. 
   
   
     19. The computer system of  claim 10 , wherein simulating the cuttings re-injection comprises generating a simulation result. 
   
   
     20. A computer system for simulating cuttings re-injection in a wellbore, comprising:
 a processor; 
 a memory; 
 a storage device; and 
 software instructions stored in the memory for enabling the computer system under control of the processor, to: 
 input at least one wellbore design parameter for the wellbore; 
 input at least one operating parameter for the cuttings re-injection; 
 input a slurry design for a slurry to be injected into the wellbore; 
 segment the wellbore into a plurality of elements, wherein each element comprising a plurality of nodes; 
 perform a simulation at a current time interval, wherein performing the simulation comprises: 
 updating a solid accumulation at a bottom of the wellbore at the current time interval; 
 performing for each of the plurality of nodes, until the wellbore reaches a steady-state condition for the current time interval, the following using the at least one wellbore design parameter, the at least one operating parameter, and the slurry design:
 calculating a sliding bed velocity; 
 calculating a suspension cross-section area using the sliding bed velocity; 
 calculating an average suspension velocity using the suspension cross-section area; 
 calculating a solid particle velocity using the average suspension velocity; and 
 calculating a solid volume concentration in suspension using the solid particle velocity; and 
 
 output the simulation results. 
 
   
   
     21. The computer system of  claim 20 , further comprising software instructions to:
 obtain a simulation result after the steady-state condition is reached; 
 determine whether the simulation result satisfies a criterion; 
 modify at least one parameter selected from a group consisting of the at least one wellbore design parameter for the wellbore, the at least one operating parameter for the cuttings re-injection, and the slurry design for a slurry to be injected into the wellbore to obtain a modified parameter; and 
 repeat the simulation at the current time interval using the modified parameter.